Applet (Flash) to illustrate different fitting methods and different model assumptions
for a very small dataset with 2 datapoints and 1 parameter.

One has 2 independent observations from the (no-intercept) model

E[y|x] = mu_{y|x} = beta times x.

The y's might represent the total numbers of
typographical errors on x randomly sampled pages of a
large document, and the data might be y=2 errors in
total in a sample of x=1 page, and y=8 errors in
total in a separate sample of x=2 pages. The beta
in the model represents the mean number of errors per
page of the document.
Or the y's might represent the
total weight of x randomly sample pages of a
document, and the data might be y=2 units of weight
in total for a sample of x=1 page, and y=8 units
for a separate sample of x=2 pages. The beta in
the model represents the mean weight per page of the document.

We gave this `estimation of beta' problem (x,y)=(1,2) & (2,8) to
several statisticians and epidemiologists, and to several grade 6 students, and
they gave us a variety of estimates, such as beta_hat = 3.6/page, 3.33/page, and 3.45!
See WHY by clicking at various locations to try out various slopes:

One must travel 7500 Km by 4-wheel jeep, over very rough terrain, with no
possibility of repairing a tire that becomes ruptured.

Suppose one starts with 14 intact tires (the 4, plus 10 spares).

On average, tires rupture at the rate of 1 per 5,000 tire-Kms (the mean interval
between ruptures is 5,000 tire-Kms). Ruptures occur independently of the of
tire position or the distance already driven with the tire (i.e., the sources of
failure are purely external). Ignore the possibility of multiple failures from a
single source, e.g. a short bad section of the trail.

SAS implementation of the 'placement' or 'U-statistics'
method described in Hanley JA and Hajian-Tilaki KO. Sampling Variability of Nonparametric
Estimates of the Areas under Receiver Operating Characteristic Curves: An Update.
Academic Radiology, 1997 4:49-58. SAS Program